Rather than going into everything I do, let me focus on two deep mysteries of fundamental physics, the nature of the Origin of Mass of elementary particles and the nature of the Dark Energy accelerating the Universe's expansion. I try to connect my theoretical work to the comprehensive and exciting experimental/observational programs underway to understand these questions.
The backdrop for the first mystery is the beautiful and very successful Standard Model of particle physics, written in the grammar of quantum mechanics and special relativity. The Higgs sector is the least tested part of the Standard Model and yet one of the most important: it is responsible for generating masses via a process known as electroweak symmetry breaking for all elementary particles! In 2012, the Large Hadron Collider outside Geneva discovered the long-awaited Higgs boson. So far its properties are in keeping with the Standard Model, but there are reasons to think that Standard Model may only be an approximation to a deeper structure of fundamental physics. The problem is that in the Standard Model, quantum effects have the tendency of making elementary particle masses either too large (by many orders of magnitude) or too small. The only way to have this theory sit in even the ballpark of the data is by an incredible "fine-tuning" of the input parameters. The general sense that this is too contrived an explanation of what we see is known as the Hierarchy Problem. So the first aspect of my work concerns the question of what types of new physics might resolve this puzzle. I have worked on several of the major proposals, Supersymmetry, Extra Spacetime Dimensions and Non-perturbative Strong Dynamics. In particular, many of the ideas I work on resonate with or originate with String Theories of Quantum Gravity (although I would not label myself a "string theorist" per se). A key insight, originating in string theory, that governs a my research is known as the AdS/CFT correspondence, relating extra dimensions and strong dynamics. A lot of my work is currently being tested by the pathbreaking experiments taking place at the Large Hadron Collider (at CERN, Geneva) and I spend considerable effort in communicating with experimentalists and trying to arrive at the best experimental search strategies.
The backdrop for the second mystery is again another extremely successful and beautiful theory, that of Big Bang cosmology and our understanding of our universe on the largest distance scales. A variety of high precision obervational measurements have made a crisis out of an ancient puzzle. They have resolved that not only is the Universe expanding, a nearly century-old discovery, but this expansion is speeding up! Part of the puzzle is that familiar forms of matter and energy can only result in a decelerating expansion. The mysterious agent of accelerating expansion has been dubbed "dark energy". The second part of the puzzle is that there is a standard candidate for dark energy, sometimes called a "cosmological constant" or sometime "vacuum energy". But quantum effects tend (as in the Higgs sector) to overshoot, they tend to give a vacuum energy many orders of magnitude too large to account for the small but now observed dark energy. This puzzle has few if any broadly accepted explanations, so much so that it is often simply ignored. Some fraction of theorists believe that our Universe is a very atypical member of a vast conglomerate of universes, a "multiverse". In this view, we find ourselves in this highly atypical universe with small vacuum energy because in any other universe with larger vacuum energy galaxies would be torn apart and there would be no life! While I find this application of the "Anthropic Principle" plausible, I like to bet against it as the full explanation in my research, and to hunt for testable mechanisms instead. I have worked on a variety of proposals for many years to see if modifications of General Relativity can tame the large quantum effects. In one early proposal of mine I called "Fat Gravity" I pointed out that a likely experimental signal of the modification would be the breakdown of Newton's Inverse Square Law at a distance of tens of microns. Such signals are presently being sought. In current work, I am working on a close analogy of this puzzle where there is a beautiful mechanism of modified gravity that can solve the puzzle. It suggests that if something similar plays out in the real world, there may be a number of cosmological measurements that would point to it. More generally, I am trying to better understand the still mysterious grammar of quantum gravity when cosmological horizons are involved, such as those that can separate different "universes". While the above two mysteries drive a lot of my research, some amount of my research is independent of these, sometimes a case of sharpening or inventing new theoretical tools that may only gain an application later, sometimes a case of understanding some physical phenomenon from already established physical laws but through a subtle derivation, new approximation, or other insight.
The central theoretical tools I use in my work are Quantum Field Theory and General Relativity, with much inspiration from String Theory. My work also relies heavily on thinking through the implications of the large body of detailed experimental data, often as massaged and made digestible by others. The wide variety of experimentalists and theorists at the University of Maryland is a fabulous resource for me.
One of my primary research accomplishments has been the development of a new class of extra-dimensional particle theory frameworks beyond the Standard Model, known as Warped Compactiications or the Randall-Sundrum model. In this framework, elementary particle properties arise in large part from their extra-dimensional wavefunctions, or profiles, as sketched here.